The story is interesting from the beginning to the end, despite sometimes being too slow for its own good (Or being too confusing). However, these are personal complaints, since this doesn't ruin the anime whatsoever. Otherwise, the animation is excellent for 2004-2005, the music captures beautifully the characters. Plus, they themselves are very interesting and extremely complex. I was rooting for most of the main cast and it was easy for me to see why the villains are how they are, either they were rotten to the core or a result of abuse and trauma.
Also, like many people, I would absolutely recommend this anime only for Johan. He's mysterious in very compelling ways, but also feels very personnal when you get to understand his view. The design of his character and his personality is one of, if not, the most well done villain I have ever saw. Naoki Urusawa did his best with Johan and Tenma's duality and I will never get tired of how he writes such realistic and compelling characters.
I used to feel bored just by seeing that Monster has 75 episodes, but please give it a try. Monster is so much more than a murder drama and now I understand why people called it a masterpiece for such a long time.